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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carry the same current II along the same direction as shown in the figure. The magnitude of force per unit length on the middle wire BB is given by:

A

μ0I22πd\frac{\mu_0 I^2}{2\pi d}

B

2μ0I2πd\frac{2\mu_0 I^2}{\pi d}

C

2μ0I22πd\frac{\sqrt{2}\mu_0 I^2}{2\pi d}

D

μ0I22πd\frac{\mu_0 I^2}{\sqrt{2}\pi d}

Step-by-Step Solution

  1. Identify the Physical Law: The magnetic force per unit length between two long, parallel current-carrying conductors separated by a distance dd is given by f=μ0I1I22πdf = \frac{\mu_0 I_1 I_2}{2\pi d} .
  2. Analyze the Geometry: In the standard configuration for this problem (NEET 2017), wire BB is at the right-angle vertex of a right-angled isosceles triangle, with wires AA and CC at the other two vertices, both at a distance dd from BB.
  3. Forces on Wire B:
  • Wire AA exerts an attractive force per unit length f1=μ0I22πdf_1 = \frac{\mu_0 I^2}{2\pi d} on BB (since the currents are in the same direction) .
  • Wire CC exerts an attractive force per unit length f2=μ0I22πdf_2 = \frac{\mu_0 I^2}{2\pi d} on BB .
  1. Vector Summation: Since the wires are arranged such that ABAB is perpendicular to BCBC, the force vectors f1\mathbf{f_1} and f2\mathbf{f_2} are mutually perpendicular. The magnitude of the resultant force per unit length is: Fnet=f12+f22=2×f=2μ0I22πdF_{net} = \sqrt{f_1^2 + f_2^2} = \sqrt{2} \times f = \sqrt{2} \frac{\mu_0 I^2}{2\pi d}
  2. Simplification: 22=12\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}, so the magnitude is μ0I22πd\frac{\mu_0 I^2}{\sqrt{2}\pi d}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMarrangementparallelstraightplacedperpendicular

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